historical semantic chaining and efﬁcient communication

Cognitive Science 40 (2016) 2081–2094Copyright © 2015 Cognitive Science Society, Inc. All rights reserved.ISSN: 0364-0213 print / 1551-6709 onlineDOI: 10.1111/cogs.12312

Historical Semantic Chaining and EfficientCommunication: The Case of Container Names

Yang Xu,a Terry Regier,b Barbara C. Maltc

aDepartment of Linguistics, University of California, BerkeleybDepartment of Linguistics, Cognitive Science Program, University of California, Berkeley

cDepartment of Psychology, Lehigh University

Received 18 March 2015; received in revised form 12 August 2015; accepted 19 August 2015

Abstract

Semantic categories in the world’s languages often reflect a historical process of chaining: Aname for one referent is extended to a conceptually related referent, and from there on to other

referents, producing a chain of exemplars that all bear the same name. The beginning and end

points of such a chain might in principle be rather dissimilar. There is also evidence supporting a

contrasting picture: Languages tend to support efficient, informative communication, often through

semantic categories in which all exemplars are similar. Here, we explore this tension through

computational analyses of existing cross-language naming and sorting data from the domain of

household containers. We find (a) formal evidence for historical semantic chaining, and (b)

evidence that systems of categories in this domain nonetheless support near-optimally efficient

communication. Our results demonstrate that semantic chaining is compatible with efficient com-

munication, and they suggest that chaining may be constrained by the functional need for efficient

communication.

Keywords: Semantic variation; Artifact categories; Semantic chaining; Historical semantics;

Semantic universals; Efficient communication

1. Introduction

Languages vary widely in the ways they partition human experience into categories.

For example, some languages use a single color term to cover both green and blue

(Berlin & Kay, 1969), and some languages have a spatial term that captures the notion of

being located in water (Levinson & Meira, 2003, p. 496), which is not captured by

any single basic spatial term in English. Yet at the same time, many logically possible

Correspondence should be sent to Yang Xu, Department of Linguistics, University of California,

Berkeley, CA 94720-2650. E-mail: [email protected]

semantic categories are not attested, and similar categories appear in unrelated

languages (e.g., Malt & Majid, 2013). What explains this pattern of wide but constrained

variation?

An existing proposal holds that this variation may be explained by the functional need

for efficient communication—that is, the need to communicate precisely, using minimal

cognitive resources. On this account, the different semantic category systems that we see

across languages constitute different structural means to this same functional end. This

idea has accounted for cross-language variation in semantic domains, including color

(Regier, Kay, & Khetarpal, 2007), kinship (Kemp & Regier, 2012), space (Khetarpal,

Neveu, Majid, Michael, & Regier, 2013), and number (Xu & Regier, 2014). It also

coheres naturally with a recent focus on efficient communication as an explanation for

other aspects of language (e.g., Fedzechkina, Jaeger, & Newport, 2012; Piantadosi, Tily,

& Gibson, 2011; Smith, Tamariz, & Kirby, 2013). Importantly for our present purposes,

in several of the above studies of semantic categories (Khetarpal et al., 2013; Regier

et al., 2007), efficient communication is shown to be supported by coherent categories in

which all exemplars tend to be similar to each other and hence tightly clustered.

This proposal appears to conflict with a well-established and influential idea: that

semantic categories reflect a historical process of chaining, whereby a name for one refer-

ent is extended to a related referent, and from there on to further referents, resulting in a

chained structure in which the later items in the chain may have little similarity to the

early ones (Brugman, 1988; Heit, 1992; Lakoff, 1987; see also Bybee, Perkins, & Pagli-

uca, 1994; Hopper & Traugott, 2003) In particular, it has been suggested that such

semantic chaining over historical time may explain the extensions of English container

names such as bottle and jar: containers are human-made artifacts that are invented in

different forms at different points in time in response to technological innovations and

current cultural needs, and the extensions of container names may reflect this historical

process (Malt, Sloman, Gennari, Shi, & Wang, 1999).

If the meanings of container names must flex to accommodate rapid changes to the

domain itself, the result may be that they are extended along dimensions that are not fully

predictable (see review by Malt, 2010). As a result, the words in this domain can denote

a wide range of objects that do not necessarily seem to be the most natural perceptual or

conceptual grouping. For example, Malt et al. (1999) found that the extensions for con-

tainer names include exemplars that are dissimilar to exemplars within the category on

average, but are very similar to certain individual exemplars, consistent with the idea of

chaining. For instance, a child’s drink container in the shape of a bear, made of plastic,

and emptied via a straw—which does not resemble a prototypical box—may nonetheless

be called a juice box. Sloman, Malt, and Fridman (2001) found that a computational

model that captures chain-like structures accounted well for container naming data from

English. These analyses examined the data without reference to historical information,

and thus did not directly assess whether the data are consistent with chaining over histori-

cal time. But they do appear to challenge the proposal that semantic systems support

communicative efficiency through categories in which exemplars tend to be similar to

each other.

2082 Y. Xu, T. Regier, B. C. Malt / Cognitive Science 40 (2016)

There is another consideration that suggests that names for containers may pattern

differently from those in other domains. In this paper, we consider the communicative

efficiency of simple container nouns such as box or bottle. Yet very often in discourse,

such container names appear with a preceding modifier of some sort (e.g., juice box,aspirin bottle). Given this usage pattern, communicative efficiency need not require that a

simple noun such as box be highly informative by itself, because the noun often appears

with a disambiguating modifier. Thus, it is possible that head nouns for containers, such

as box or bottle, may not support efficient communication, even if the regularly appearing

modified forms juice box or aspirin bottle do.

Two important questions are left open. First, is there evidence for a genuinely histori-

cal process of chaining in modern semantic systems such as those of container names?

And second, if so, does chaining in this domain in fact prevent efficient communication?

Or are the lexical categories of this domain, like those of other domains, shaped by the

need for efficient communication, despite semantic chaining? The studies we present

address these questions.

In what follows, we summarize the theory of efficient communication, and demonstrate

that chaining is in principle a challenge to this theory. We also briefly describe the cross-

language data on which we rely. We then present two studies based on those data. The

first study tests for historical chaining in the naming of containers, and the second study

tests whether container naming across languages is communicatively efficient, in the

sense of having tightly clustered, coherent semantic category membership. To preview

our results, we find evidence for historical chaining, yet we also find that despite this

chaining, the container naming systems of three languages all support near-optimally

informative communication. We speculate that semantic chaining may be constrained by

the need for categories to be informative.

2. Formal presentation of theory

In this section, we present the theory of efficient communication in formal terms. We

then demonstrate that chaining can in principle lead to inefficient communication.

Consider the communicative scenario of Fig. 1. Here, the speaker has a target

object in mind—in this case, a specific kind of bottle—and wishes to communicate

that referent to the listener. To that end, the speaker utters the word bottle. Given that

utterance, the listener then attempts to mentally reconstruct the speaker’s intended

meaning. Because the word bottle covers a range of possible objects, the listener’s

representation is inexact and is shown as a probability distribution extending over that

range. We take a communicative system to be informative to the extent that it sup-

ports accurate mental reconstruction by the listener of the speaker’s intended meaning;

that is, reconstruction that is as exact as possible. While the listener need not always

reconstruct exactly the referent the speaker has in mind for communication to succeed

(Connell & Lynott, 2014; Ferreira, Bailey, & Ferraro, 2002), if the speaker utters

Y. Xu, T. Regier, B. C. Malt / Cognitive Science 40 (2016) 2083

bottle having in mind a baby bottle and the listener thinks of a Coke or wine bottle,

unintended consequences may result.

We model the mental representations of both speaker and listener as probability distri-

butions. Unlike the listener’s distribution, the speaker’s distribution S is certain: It con-

sists of a point mass centered on the target, capturing our assumption that the speaker is

certain of the meaning she wishes to convey. Following Regier, Kemp, and Kay’s (2015)

analysis of color naming, we take the listener distribution L(i) to be based on the similar-

ity (assessed empirically) of exemplar i to all exemplars in the category named by the

word w:

LðiÞ /X

j2wsimði; jÞ ð1Þ

We then take the unit communicative cost C(i) of communicating about a target object

i using a particular communicative system to be a measure of the discrepancy between

the listener distribution L and the speaker distribution S: specifically the Kullback–Leiblerdivergence DKLðSjLÞ between these two distributions. In the case of speaker certainty, this

reduces to surprisal (Tribus, 1961):

CðiÞ ¼ DKLðSjjLÞ ¼X

j

SðjÞ log2SðjÞLðjÞ ¼ log2

1

LðiÞ ð2Þ

“bottle”

Speaker Listener

Fig. 1. A simple communicative scenario.


Finally, we take the overall communicative cost of a system to be the expected

communicative cost incurred in communicating about the domain (Kemp & Regier,

2012). This is the sum of the unit costs of all possible targets in the domain, each

weighted by its relative frequency of occurrence in usage, or need probability N(i)(assessed empirically):

E½C� ¼X

i

CðiÞNðiÞ ð3Þ

We take a communicative system to be informative to the extent that it exhibits low

communicative cost E[C]. We take the complexity of a system to be the number of lexi-

cal categories in the system. Finally, we take a system of categories to be communica-tively efficient to the extent that it it is more informative than most logically possible

hypothetical systems of the same complexity.

2.1. Chaining and inefficient communication

Semantic chaining can give rise to inefficient communication, as illustrated in Fig. 2.

Panel (a) of this figure shows two artificial category systems that partition the same set of

eight objects (shown as black dots). The category system in the left half of the panel

divides these objects into two non-chained (or clustered) categories. The system in the

right half of the panel divides the same set of objects into two chained categories. The

complexity of the two systems is the same (two categories in each system), but they dif-

fer in informativeness. Panel (b) shows the communicative costs of these two systems,

compared with the costs of all possible partitions of the eight objects into two groups of

size 4.1 It can be seen that relative to these hypothetical systems, the non-chained system

from panel (a) is optimally informative for this level of complexity, and thus communica-

tively efficient, whereas the chained system is not. This demonstrates that semantic chain-

ing has the potential to yield inefficient communication, as formalized here.

2.4 2.6 2.80

1

2

3

4

5

6

7

Communicative cost

Num

ber o

f sys

tem

s

HypotheticalNon−chainedChainedNon−chained categories Chained categories

A B

A

B

(A) (B)

Fig. 2. Chaining and communicative inefficiency. (a) Non-chained and chained systems of equal complexity

(two categories each). (b) Communicative costs of these systems and hypothetical systems of equal complexity.


3. Data

We reanalyze data from Malt et al. (1999) on the naming and perceived similarity of

household containers. The stimulus set for this research consisted of photographs of 60

household containers, representing a wide range of bottles, jars, and similar containers.

Fig. 3 shows a sample of these objects.

We used two types of data that had been collected relative to this stimulus set. The

first type is linguistic. Native speakers of American English, Mandarin Chinese, and

Argentinian Spanish were instructed to name each container stimulus in their native

language, giving whatever name they felt was best or most natural.2 We took the most

frequently produced (modal) name for each object as its name in the given language. The

second type of data is from a pile-sorting task. We used these data to construct a similar-

ity space of the 60 container objects in our stimulus set. In particular, we used pile-sort-

ing by English and Chinese speakers from the study by Malt et al. (1999) (the groups for

which data were retrievable), and we focused on sorting based on overall similarity of

the containers (i.e., participants were allowed to sort freely, using both the physical attri-

butes and functions of the containers, as they saw fit). Since the pile sorts correlated

highly across groups (Malt et al., 1999), we aggregated pile-sorting responses from

participants across the two groups, and took the similarity sim(i,j) of any two objects iand j to be the proportion of all participants who sorted those two objects into the same

Fig. 3. Sample stimuli from Malt et al. (1999).


pile. If two objects are always co-sorted together across participants, their similarity

would be 1. If two objects are never co-sorted, their similarity would be 0. We used this

60 9 60 similarity matrix as a proxy for a universal conceptual space. Malt et al. (1999)

showed a high degree of correlation of these similarity matrices between each pairing of

the three language groups in our study (see also Ameel, Storms, Malt, & Sloman, 2005,

and Malt et al., 2014, for high sorting correlations across language groups for other

stimulus sets). These naming and similarity measures were used in our analyses below.

4. Study 1: Historical chaining

In our first study, we asked whether these data provide evidence for historical chaining.

That is, has the current extension of the names been developed through a chain of uses

expanding over historical time? We test for historical chaining over all three languages in

the dataset.

We considered three categorization models, specified in Table 1: a chaining model, a

clustering model, and a majority vote model. The chaining model is a nearest-neighbor

(or 1-nearest-neighbor) model, which assigns a target item to the category that includes

the exemplar most similar to that target item; this is the model that was explored by

Sloman et al. (2001). The clustering model is based on Eq. 1 and assigns a target item to

the category whose exemplars exhibit the greatest similarity to the target overall. The

majority vote model is a baseline model that assigns a target item to the category that

has the most exemplars, without reference to any intrinsic relations among exemplars.

Similarities sim(i,j) were determined by the pile-sort data. The category (word) w for each

container object was determined by the modal head noun that was used to label it in the

naming data; for example, the category for juice bottle would be bottle in English.

Each model was tested against the data in a manner that recapitulates the addition of

new exemplars to categories over historical time. We began by time-stamping the name

of each container item, providing an estimate of when that item appeared in history. We

obtained these time stamps from a large historical corpus, the Google Ngram American

English corpus (Michel et al., 2011), using a computational procedure described in the

Supplementary Material. Following this procedure, we then simulated the sequential

emergence of all 60 exemplars in history and asked which of the three models specified

above best accounted for categorizations found in the naming data.

Table 1

Summary of models. In the rules below, i is the target exemplar, j is any exemplar other than i, w is a lexical

category, sim(�,�) is the similarity between two exemplars, and |w| is the size of category w

Model Categorization Rule

Chaining i? the category w of arg maxjsim(i,j)Clustering i ! arg maxw

Pj2w simði; jÞ

Majority vote i ! arg maxw jwj


For each model, this predictive analysis proceeded as follows. We first seeded the

model with the object that first appeared in history, based on appearance of the corre-

sponding phrase in the corpus; this object was “glass bottle.” As each remaining object

became available (based on appearance of its name in the corpus), we used the model to

predict its category membership, based only on items already encountered and holding

out the category labels for the current item and all upcoming items. The category label

was always the head noun associated with that object (e.g., box rather than juice box).Whenever the model mispredicted the category membership of an item because the

object’s name was not yet represented by already-considered exemplars, we introduced

that label and thus expanded the repertoire of categories that the model had to choose

from among beyond that point in time. We then asked which model best predicted the

data, when presented in historical order.

Fig. 4 summarizes the predictive accuracies of these models. The results show that in

general, the chaining model accounts for the data better than the two alternative models

in all three languages. Specifically, we found the chaining model to outperform the

clustering model by about 8%, 3%, and 10% for English, Spanish, and Chinese, respec-

tively (and to outperform the majority vote model by 23%, 35%, and 62% for the three

languages). We observed that although the chaining model makes largely similar predic-

tions to the clustering model (the two models overlap in approximately 65% of their

predictions within each of the three languages), they are different in interesting ways.

Concretely, in the case of English, we observed that the following historical chain of

exemplars (dates included in parentheses) was predicted accurately by the chaining model

but not by the clustering model: olive jar (1903) ? jelly jar (1925) ? peanut butter jar

0

10

20

30

40

50

60

70

80

90

100

English Spanish Chinese

Pre

dict

ive

accu

racy

(%

)

ChainingChaining (randomized)ClusteringMajority vote

Fig. 4. Summary of historical analysis of chaining. Error bars (standard error) are shown only for the case

of randomized chaining, as that is the only case in which multiple simulations were run.


(1945) ? peanut jar (1963) ? applesauce jar (1970). Conversely, the clustering model

—but not the chaining model—was correct in predicting the category labels of a small

number of exemplars such as film container (1912) and squeeze bottle (1942).

We sought to determine whether the chaining model’s superiority over the clustering

model on our data is due to an exceptionally good match between the chaining model

and the structure of our data. If so, we would expect the superiority of the chaining

model over the clustering model to be greater when assessed relative to our data than

when assessed relative to hypothetical variants of our data. A statistical analysis described

in the Supplementary Material supports this prediction. We also wished to test whether

the good fit of the chaining model is dependent on the historical time-stamps provided by

our corpus searches. Would the same chaining model with different time stamps perform

as well? To test this, we re-ran the chaining model, but with the temporal sequence of

exemplars randomized while keeping the category labels the same. We ran 100,000 such

randomized sequences for each language. For all three languages, the mean prediction of

the chaining model on the randomized historical sequences was significantly worse than

with the real historical sequence (p < .01 via standard permutation tests), indicating that

the success of this model does reflect the actual historical emergence of these items.

These results demonstrate that the chaining model accounts well for the diachronic

development of the extension of container names. This outcome supports the proposal

that historical semantic chaining is involved in the formation of container lexical

categories.

Fig. 5 illustrates the historical semantic chaining in the development of the English

category bottle, on our analysis. We observe that chaining in this real-world category is

bottle of vitamins(1939)

bottle of aspirin (1922)

iodine bottle (1857)

plastic bottle (1952)

squeeze bottle (1942)baby bottle (1928)

glass bottle (1801)

spray bottle (1962)

detergent bottle (1954)

Fig. 5. Semantic chaining in the English bottle category. Container names are annotated with dates identified

from the corpus searches. Spatial proximity between two items roughly corresponds to their judged similarity.

Arrows indicate the trajectory traced by the chaining model.


interestingly different from the idealized case we considered earlier in Fig. 2. Instead of

forming a long chain, “natural” semantic chaining in this instance takes the form of short

chains grounded in hub exemplars (e.g., iodine bottle and baby bottle), which form local

clusters within the category. Whether such natural chaining structures support efficient

communication is a question we will test in the next study.

5. Study 2: Chaining and efficient communication

We have seen that semantic chaining has the potential to yield inefficient communica-

tion, and that the container naming data of Malt et al. (1999) show evidence of semantic

chaining over time. Left unaddressed is whether this natural semantic chaining in fact

prevents efficient, informative communication.

The data of Malt et al. (1999) have not previously been analyzed with respect to

whether the lexical categories support efficient communication about containers. We con-

duct that analysis here, separately for each of the three languages (English, Spanish, and

Chinese), using the computational formulation of efficient communication specified

above. As before, we took the category system of each language to be determined by the

modal head noun that was used to label it in the naming data, and we took similarities

sim(i,j) to be determined by the pile-sort data. We estimated the need probability N(i) foreach item i using frequencies of container names (modifier + head noun) from the Google

Ngram American English corpus; specifically, we took frequencies at year 1999, which

matches the year of publication of the original work by Malt et al. (1999). We then

applied Eqs. 1–3 to obtain the communicative cost for the container naming system in

each language.

We take a category system to be near-optimally efficient if it is more informative than

most hypothetical systems with the same number of categories. Thus, in order to assess

the communicative efficiency of the English, Spanish, and Chinese container naming sys-

tems, we need to compare the communicative cost of each to the costs of a large set of

hypothetical systems with the same number of categories as those reported by Malt et al.

(1999) for this stimulus set (English: 7 categories; Spanish: 15 categories; Chinese: 5

categories). We also constrained the size of each category in a hypothetical system to be

equivalent to that in the corresponding attested target system; this constraint ensures that

attested and hypothetical categories are identical in number and size, and differ only in

the exemplars that are assigned to those categories.

Concretely, for each target language (English, Spanish, Chinese), we constructed

hypothetical comparison systems through simulated chaining in similarity space (cf. Khe-

tarpal et al., 2013), as follows. We began by randomly choosing an initial exemplar and

assigning an arbitrary category to it. We then extended that name to a new exemplar,

which was selected by sampling exemplars in proportion to their similarity with the exist-

ing exemplar. We then repeated this chaining process, where the probability of a category

name being chosen for expansion was proportional to the number of remaining (as-yet-

unlabeled) exemplars in that category. This process continued until we had assigned each


exemplar to a category, such that each category had the same number of exemplars as in

the attested target system. This procedure effectively generated a hypothetical chained

system in the same similarity space as an attested system. Our use of chained systems as

hypothetical competitors provides a conservative test, because it excludes from considera-

tion unnatural-seeming but logically possible hypothetical systems with disconnected

(non-contiguous) categories. Recall that in Fig. 2, although chained systems were not

highly informative, they were more informative than many other hypothetical systems

that are excluded from consideration here.

For each of the three target languages, we created 100,000 such hypothetical chained

systems. We then compared the communicative cost of the attested target language to the

costs of the hypothetical systems using the formulation presented earlier. The results are

shown in Fig. 6.

Each of the three attested systems is significantly less costly than its corresponding

class of hypothetical chained systems (English: p < .001; Spanish: p < .0001; Chinese:

p < .03). We conclude from these results that although these systems do exhibit semantic

chaining, each of them is nevertheless highly informative—and thus tightly clustered—relative to a large class of comparable hypothetical chained systems.

6. Discussion

In this paper, we have presented two related contributions. First, we have provided

what is, to our knowledge, the first computational demonstration of historical semantic

chaining in a modern semantic system, using a large corpus of historical text. Second, we

have shown that names for household containers in English, Spanish, and Chinese all

support highly informative communication, despite the presence of historical chaining in

this domain and the potential of chaining to prevent informative communication.

4.5 5 5.5 60

0.5

1

1.5

2x 10

4 English

Num

ber

of s

yste

ms

Communicative cost

Attested

Hypothetical

4 4.5 5 5.50

0.5

1

1.5

2x 10

4 Spanish

5 5.2 5.4 5.6 5.80

0.5

1

1.5

2x 10

4 Chinese

Fig. 6. Efficiency analysis of container naming systems in English, Spanish, and Chinese. In each case, the

attested system exhibits low communicative cost (high informativeness) relative to a large set of hypothetical

systems of equal complexity.


Our results concern simple nouns for containers, such as bottle or box, even though

these often appear in discourse in modifier-noun combinations such as aspirin bottle or

juice box. The fact that these nouns often appear with a modifier that narrows the

intended semantic range might be taken to imply that bare nouns for containers do not by

themselves support highly informative communication in the sense identified here,

because much of the informativeness is often supplied by the modifier. But our results

suggest that these bare nouns are nonetheless near-optimally informative. What are we to

make of this? A relevant consideration is that we have shown that systems of bare con-

tainer nouns across languages are near-optimally informative relative to other possible

systems of the same complexity—that is, with the same number of separate container

words. It is possible that such a system could be nearly as informative as possible for its

level of complexity, yet still be inadequately semantically fine-grained to support the

needs of daily communication, which often require the addition of a modifier. Our results

suggest this interpretation. On this view, the finding of interest is that a system of general

categories (bare nouns)—the informativeness of which is often enhanced by the use of a

modifier in discourse—nonetheless appears to bear the stamp of communicative pressure

when considered without these modifiers.

Our findings leave a number of questions open. How general is the phenomenon of

historical chaining, and the nature of it that we have suggested here? Does chaining

appear in similar “hub exemplars plus short chains” form in other domains? How general

is our finding that historical chaining may be constrained by communicative forces?

Future studies can address these questions by applying analyses similar to ours to other

domains, as well as new models and analyses, to explore the linguistic packaging of

meaning across languages and across time.

Acknowledgments

This research was supported by NSF award SBE-1041707 to the Spatial Intelligence

and Learning Center (SILC). We thank Charles Kemp for earlier ideas on chaining and

Rob Kass for the concept of change-point detection.

Notes

1. In computing cost, we assumed that the distance between horizontally or vertically

neighboring objects in the grid is 1, that the similarity between any two objects i,jis sim(i,j) = exp (�distance(i,j)), and that need probability N(i) is uniform across

all objects i.2. Naming data were collected from 28 native speakers of English, all students at

Lehigh University in the United States; 51 native speakers of Spanish, all from

Comahue National University in Argentina; and 50 native speakers of Mandarin


Chinese, 10 of whom were students at Lehigh and 40 of whom were students at

Shanghai University in China.

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Supporting Information

Additional Supporting Information may be found in

the online version of this article:

Appendix S1. Supplementary material


historical semantic chaining and efﬁcient communication

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